lasd0(3)

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version 3.12.1 · 9 versions
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NAME 🎀

okay bestie, this is lasd0(3) from the Library Functions Manual — manual name folded in cute near the top, no boring header copy. The NAME tea is: lasd0 - lasd0: D&C step: top level solver 💅

SYNOPSIS ✨

Functions

dlasd0 — signature, exactly:

subroutine dlasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info)

DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc. 🔥

slasd0 — signature, exactly:

subroutine slasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info)

SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc. 💖

Detailed Description 🫶

(no extra prose here in the original — just the function docs below, bestie. The real main-character energy is in Function Documentation.)

Function Documentation 👑

subroutine dlasd0 👑

subroutine dlasd0 (integer n, integer sqre, double precision, dimension( * )
    d, double precision, dimension( * ) e, double precision, dimension( ldu,
    * ) u, integer ldu, double precision, dimension( ldvt, * ) vt, integer
    ldvt, integer smlsiz, integer, dimension( * ) iwork, double precision,
    dimension( * ) work, integer info)

DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.

Purpose 🌟

Using a divide and conquer approach, DLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE. The algorithm computes orthogonal matrices U and VT such that B = U * S * VT. The singular values S are overwritten on D.

A related subroutine, DLASDA, computes only the singular values, and optionally, the singular vectors in compact form. 💫

Parameters 🧮

  • N — N is INTEGER. On entry, the row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D.
  • SQRE — SQRE is INTEGER. Specifies the column dimension of the bidiagonal matrix. = 0: The bidiagonal matrix has column dimension M = N; = 1: The bidiagonal matrix has column dimension M = N+1;
  • D — D is DOUBLE PRECISION array, dimension (N). On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO = 0, contains its singular values.
  • E — E is DOUBLE PRECISION array, dimension (M-1). Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed. 😭
  • U — U is DOUBLE PRECISION array, dimension (LDU, N). On exit, U contains the left singular vectors, if U passed in as (N, N) Identity.
  • LDU — LDU is INTEGER. On entry, leading dimension of U.
  • VT — VT is DOUBLE PRECISION array, dimension (LDVT, M). On exit, VT**T contains the right singular vectors, if VT passed in as (M, M) Identity.
  • LDVT — LDVT is INTEGER. On entry, leading dimension of VT.
  • SMLSIZ — SMLSIZ is INTEGER. On entry, maximum size of the subproblems at the bottom of the computation tree.
  • IWORK — IWORK is INTEGER array, dimension (8*N).
  • WORK — WORK is DOUBLE PRECISION array, dimension (3*M**2+2*M).
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, a singular value did not converge.

Author 🫶

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Contributors 💖

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 150 of file dlasd0.f.

subroutine slasd0 👑

subroutine slasd0 (integer n, integer sqre, real, dimension( * ) d, real,
    dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real,
    dimension( ldvt, * ) vt, integer ldvt, integer smlsiz, integer,
    dimension( * ) iwork, real, dimension( * ) work, integer info)

SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.

Purpose 🌟

Using a divide and conquer approach, SLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE. The algorithm computes orthogonal matrices U and VT such that B = U * S * VT. The singular values S are overwritten on D.

A related subroutine, SLASDA, computes only the singular values, and optionally, the singular vectors in compact form. 💫

Parameters 🧮

  • N — N is INTEGER. On entry, the row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D.
  • SQRE — SQRE is INTEGER. Specifies the column dimension of the bidiagonal matrix. = 0: The bidiagonal matrix has column dimension M = N; = 1: The bidiagonal matrix has column dimension M = N+1;
  • D — D is REAL array, dimension (N). On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO = 0, contains its singular values.
  • E — E is REAL array, dimension (M-1). Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed. 😭
  • U — U is REAL array, dimension (LDU, N). On exit, U contains the left singular vectors, if U passed in as (N, N) Identity.
  • LDU — LDU is INTEGER. On entry, leading dimension of U.
  • VT — VT is REAL array, dimension (LDVT, M). On exit, VT**T contains the right singular vectors, if VT passed in as (M, M) Identity.
  • LDVT — LDVT is INTEGER. On entry, leading dimension of VT.
  • SMLSIZ — SMLSIZ is INTEGER. On entry, maximum size of the subproblems at the bottom of the computation tree.
  • IWORK — IWORK is INTEGER array, dimension (8*N).
  • WORK — WORK is REAL array, dimension (3*M**2+2*M).
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, a singular value did not converge.

Author 🫶

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Contributors 💖

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 150 of file slasd0.f.

Author 💅

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